# defining gcd on rings

I see that in most textbooks they say let $R$ be an integral domain and start defining the greatest common divisor. My question is, can gcd's be defined on just commutative rings without an identity?

• – Jose Arnaldo Bebita-Dris Feb 12 '16 at 11:48
• An example would be the ring of all even integer (i.e. $2\mathbb{Z}$) and the usual GCD. – gammatester Feb 12 '16 at 11:53